Effects of strongly variable viscosity on three-dimensional compressible convection in planetary mantles

Journal of Geophysical Research: Solid Earth

Volumn 101, Issue 2, 1996, Pages 3311-3332

  Tackley, Paul J ^a,b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSIBILITY; CONVECTION; MANTLE; RHEOLOGY; TEMPERATURE; VISCOSITY;

EID: 0029729204     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1029/95jb03211     Document Type: Article

References (120)

1. Anderson, D.L., A seismic equation of state, II., Shear properties and thermodynamics of the lower mantle, Phys. Earth Planet. Inter., 45 , 307-323 , 1987.
2. Anderson, O.L., H. Oda, and D. Isaak, A model for the computation of thermal expansivity at high compression and high temperatures: MgO as an example, Geophys. Res. Lett., 19, 1987-1990, 1992.
3. Backus, G.E., Gross thermodynamics of heat engines in the deep interior of the Earth, Proc. Natl. Acad. Sci. U.S.A., 72, 1555-1558, 1975.
4. Balachandar, S., and D.A. Yuen, Time-dependent three-dimensional compressible convection with depth-dependent properties, Geophys. Res. Lett., 19, 2247-2250, 1992.
5. Balachandar, S., D.A. Yuen, and D. Reuteler, Viscous and adiabatic heating effects in 3-dimensional compressible convection at infinite Prandtl number, Phys. Fluids A, 5, 2938-2945, 1993.
6. Balachandar, S., D.A. Yuen, and D.M. Reuteler, Localization of toroidal motion and shear heating in 3-D high Rayleigh number convection with temperature dependent viscosity. Geophys. Res. Lett., 22, 477-480, 1995a.
7. Balachandar, S., D.A. Yuen, D.M. Reuteler, and G.S. Lauer, Viscous dissipation in 3-dimensional convection with temperature dependent viscosity, Science, 267, 1150-1153, 1995b.
8. Baumgardner, J.R., Three-dimensional treatment of convective flow in the Earth's mantle, J. Stat. Phys., 39, 501-511, 1985.
9. Baumgardner, J.R., Application of supercomputers to 3-D mantle convection, in The Physics of the Planets, edited by S.K. Runcorn, pp. 199-231, John Wiley, New York, 1988.
10. Bercovici, D., A simple model of plate generation from mantle flow, Geophys. J. Int., 114, 635-650, 1993.
11. Bercovici, D., A source-sink model of the generation of plate tectonics from non-Newtonian mantle flow, J. Geophys. Res., 100, 2013-2030, 1995.
12. Bercovici, D., G. Schubert, and G.A. Glatzmaier, Influence of heating mode on three-dimensional mantle convection, Geophys. Res. Lett., 16, 617-620, 1989a.
13. Bercovici, D., G. Schubert, and G.A. Glatzmaier, Three-dimensional spherical models of convection in the Earth's mantle, Science, 244, 893-1016, 1989b.
14. Bercovici, D., G. Schubert, G.A. Glatzmaier, and A. Zebib, Three-dimensional convection in a spherical shell, J. Fluid Mech., 206, 75-204, 1989c.
15. Bercovici, D., G. Schubert, and G.A. Glatzmaier, Three-dimensional convection of an infinite-Prandtl-number compressible fluid in a basally heated spherical shell, J. Fluid Mech., 239, 683-719, 1992.
16. Bindschadler, D.L., G. Schubert, and W.M. Kaula, Coldspots and hotspots: Global tectonics and mantle dynamics of Venus, J Geophys. Res., 97, 13,495-13,532, 1992.
17. Blankenbach, B., et al., A benchmark comparison for mantle convection codes, Geophys. J. Int., 98, 23-38, 1989.
18. Booker, J.R., Thermal convection with strongly temperature dependent viscosity, J. Fluid Mech., 76, 741-754, 1976.
19. Boussinesq, J., Théorie Analytique de la Chaleur Mise en Harmonie Avec la Thermodynamique et avec la Théorie Mécanique de la Lumière, vol. II, pp. 157-176, Gauthier-Villars, Paris, 1903.
20. Brandt, A., Guide to multigrid development, in Multigrid Methods: Proceedings Koln-Porz. 1981, Lecture Notes in Mathematics, edited by W. Hackbusch and U. Trottenberg, pp 220-312, Springer-Verlag, New York, 1982.
21. Breuer, D., and T. Spohn, Cooling of the Earth, Urey ratios, and the problem of potassium in the core, Geophys. Res. Lett., 20, 1655-1658, 1993.
22. Busse, F.H., On the stability of two-dimensional convection in a layer heated from below, J. Math. Phys., 46, 140-150, 1967.
23. Busse, F.H., and H. Frick, Square-pattern convection in fluids with strongly temperature dependent viscosity, J. Fluid Mech., 150, 451-465, 1985.
24. Busse, F. H., et al., 3D convection at infinite Prandtl number in Cartesian geometry - A benchmark comparison, Geophys. Astrophys. Fluid Dyn., 75, 39-59, 1994.
25. Carrigan, C.R., Convection in an internally heated, high Prandtl number fluid: A laboratory study, Geophys. Astrophys. Fluid Dyn., 32, 1-21, 1985.
26. Chopelas, A., and R. Boehler, Thermal expansivity in the lower mantle, Geophys. Res. Lett., 19, 1983-1986, 1992.
27. Christensen, U.R., Convection with pressure- and temperature dependent non-Newtonian rheology, Geophys. J. R. Astron. Soc., 77, 343-384, 1984.
28. Christensen, U.R., Heat transport by variable viscosity convection, II; Pressure influence, non-Newtonian rheology and decaying heat sources, Phys. Earth Planet. Inter., 37, 183-205, 1985.
29. Christensen, U., and H. Harder, 3-D convection with variable viscosity, Geophys. J. Int., 104, 213-226, 1991.
30. Christensen, U. R., and D. A. Yuen, Time-dependent convection with non-Newtonian viscosity, J. Geophys. Res., 94, 814-820, 1989.
31. Cserepes, L., Numerical studies of non-Newtonian mantle convection, Phys. Earth Planet. Inter., 30, 49-61, 1982.
32. Cserepes, L., and U. Christensen, Three-dimensional convection under drifting plates, Geophys. Res. Lett., 17, 1497-1500, 1990.
33. Cserepes, L., M. Rabinowicz, and C. Rosemberg-Borot, Three-dimensional infinite Prandtl number convection in one and two layers with implications for the Earth's gravity field, J. Geophys. Res., 93, 12,009-12,025, 1988.
34. Davies, G.F., Ocean bathymetry and mantle convection, 1, Large-scale flow and hotspots, J. Geophys. Res., 93, 10467-10480, 1988.
35. Davies, G.F., and M.A. Richards, Mantle convection, J. Geology, 100, 151-206, 1992.
36. Duffy, T.S., and T.J. Ahrens, Thermal expansion of mantle and core materials at very high pressures, Geophys. Res. Lett., 20, 1103-1106, 1993.
37. Duncan, R.A., and M.A. Richards, Hotspots, mantle plumes, flood basalts, and true polar wander, Rev. Geophys., 29, 31-50, 1991.
38. Durham, W.B., C. Froidevaux, and O. Jaoul, Transient and steady state creep of pure forsterite at low stress, Phys. Earth Planet. Inter., 19, 263-274, 1979.
39. Dziewonski, A.M., and D.L. Anderson, Preliminary reference Earth model, Phys. Earth Planet. Inter., 25, 297-356, 1981.
40. Forte, A.M., A.M. Dziewonski, and R.L. Woodward, Aspherical structure of the mantle, tectonic plate motions, nonhydrostatic geoid, and topography of the core-mantle boundary, in Dynamics of the Earth's Deep Interior and Earth Rotation, Geophys. Monogr., vol 72, edited by J.L. LeMouel, D.E. Smylie, and T. Herring, pp. 135-166, AGU, Washington, D.C., 1993.
41. Frick, H., F.H. Busse, and R.M. Clever, Steady three-dimensional convection at high Prandtl numbers, J. Fluid Mech., 127, 141-153, 1983.
42. Fukao, Y., Seismic tomogram of the Earth's mantle: Geodynamic implications, Science, 258, 625-630, 1992.
43. Gable, C.W., R.J. O'Connell, and B.J. Travis, Convection in three dimensions with surface plates: Generation of toroidal flow, J. Geophys. Res., 96, 8391-8405, 1991.
44. Giannandrea, E., and U. Christensen, Variable viscosity convection experiments with a stress-free upper boundary and implications for the heat transport in the Earth's mantle, Phys. Earth Planet. Inter., 78, 139-152, 1993.
45. Glatzmaier, G.A., Numerical simulations of mantle convection: Time-dependent, three-dimensional, compressible, spherical shell, Geophys. Astrophys. Fluid Dyn., 43, 223-264, 1988.
46. Glatzmaier, G.A., and G. Schubert, Three-dimensional spherical models of layered and whole mantle convection, J. Geophys. Res., 98, 21,969-21,976, 1993.
47. Glatzmaier, G.A., G. Schubert, and D. Bercovici, Chaotic, subduction-like downflows in a spherical model of convection in the Earth's mantle, Nature, 347, 274-277, 1990.
48. Griffiths, R.W., and I.H. Campbell, Stirring and structure in mantle plumes, Earth Planet. Sci. Lett., 99, 66-78, 1990.
49. Gurnis, M., and G.F. Davies, Numerical study of high Rayleigh number convection in a medium with depth-dependent viscosity, Geophys. J. R. Astron. Soc., 85, 523-541, 1986.
50. Hager, B.H., and M.A. Richards, Long-wavelength variations in Earth's geoid: Physical models and dynamical implications. Philos. Trans. R. Soc. London., 328, 309-327, 1989.
51. Hansen, U., D.A. Yuen, S.E. Kroening, and T.B. Larsen, Dynamical consequences of depth-dependent thermal expansivity and viscosity on mantle circulations and thermal structure, Phys. Earth Planet. Inter., 77, 205-223, 1993.
52. Hewitt, J.M., D.P. McKenzie, and N.O. Weiss, Dissipative heating in convective flows, J. Fluid Mech., 68, 721-738, 1975.
53. Honda, S., D.A. Yuen, S. Balachandar, and D. Reuteler, Three-dimensional instabilities of mantle convection with multiple phase transitions, Science, 259, 1308-1311, 1993.
54. Houseman, G., The dependence of convection planform on mode of heating, Nature, 332, 346-349, 1988.
55. Howard, L.N., Convection at high Rayleigh number, in Proceedings of the Eleventh International Congress of Applied Mechanics, edited by H. Gortler, pp. 1109-1115, Springer-Verlag, New York, 1966.
56. Jarvis, G.T., and D.P. McKenzie, Convection in a compressible fluid with infinite Prandtl number, J. Fluid Mech., 96, 515-583, 1980.
57. Jarvis, G.T., and W.R. Peltier, Convection models and geophysical observations, in Mantle Convection: Plate Tectonics and Global Dynamics edited by W.R. Peltier, pp. 479-594, Gordon and Breach, New York, 1989.
58. Karato, S., and P. Li, Diffusion creep in perovskite - Implications for the rheology of the lower mantle, Science, 255, 1238-1240, 1992.
59. Karato, S., and P. Wu, Rheology of the upper mantle: A synthesis, Science, 260, 771-778, 1993.
60. Kiefer, W.S., and B.H. Hager, Mantle downwelling and crustal convergence - A model for Ishtar Terra, Venus, J. Geophys. Res., 96, 967-980, 1991.
61. King, S. D., and G.T. Masters, An inversion for radial viscosity structure using seismic tomography, Geophys. Res. Lett., 19 , 1551-1554, 1992.
62. Kirby, S.H., and A.K. Kronenberg, Rheology of the lithosphere: Selected topics, in US National Report to International Union of Geodesy and Geophysics 1983-1986, Contributions in Tectonophysics, pp. 1219-1244, AGU, Washington, D.C., 1987.
63. Leitch, A.M., D.A. Yuen, and G. Sewell, Mantle convection with internal heating and pressure-dependent thermal expansivity. Earth Planet. Sci. Lett., 102, 213-232, 1991.
64. Loper, D.E., Mantle plumes, Tectonophysics, 187, 373-384, 1991.
65. Machetel, P., M. Rabinowicz, and P. Bernardet, Three-dimensional convection in spherical shells, Geophys. Astrophys. Fluid Dyn., 37, 57-84, 1986.
66. Malevsky, A. V., and D. A. Yuen, Strongly chaotic non-Newtonian mantle convection, Geophys. Astrophys. Fluid Dyn., 65 , 149-171, 1992.
67. Malevsky, A.V., and D.A. Yuen, Plume structures in the hard-turbulent regime of three-dimensional infinite Prandtl number convection, Geophys. Res. Lett., 20, 383-386, 1993.
68. Meade, C., and R. Jeanloz, The strength of mantle silicates at high pressures and room temperature: Implications for the viscosity of the mantle, Nature, 348, 533-535, 1990.
69. Mitrovica, J.X., and W.R. Peltier, The inference of mantle viscosity from an inversion of the Fennoscandian relaxation data, Geophys. J. Int, 114, 45-62, 1993.
70. Moresi, L.-N., and V.S. Solomatov, Numerical investigations of 2D convection with extremely large viscosity variations, Phys. Fluids, 7, 2154-2162, 1995.
71. Nataf, H.-C., Mantle convection, plates, and hotspots, Tectonophysics, 187, 361-371, 1991.
72. Ogawa, M., G. Schubert, and A. Zebib, Numerical simulations of three-dimensional thermal convection in a fluid with strongly temperature dependent viscosity, J. Fluid Mech., 233, 299-328, 1991.
73. Olson, P., An experimental approach to thermal convection in a two-layered mantle, J. Geophys. Res., 89, 11293-11301, 1984.
74. Olson, P., G. Schubert, and C. Anderson, Plumes formation in the D" layer and the roughness of the core-mantle boundary, Nature, 327, 409-413, 1987.
75. Olson, P., G. Schubert, and C. Anderson, Structure of axisymmetric mantle plumes, J. Geophys. Res., 98, 6829-6844, 1993.
76. 3 perovskite, Geophys. Res. Lett., 18, 239-242, 1991.
77. Parmentier, E.M., C. Sotin, and B.J. Travis, Turbulent 3D thermal convection in an infinite Prandtl number, volumetrically heated fluid: Implications for mantle dynamics, Geophys. J. Int., 116, 241-251, 1994.
78. Patankar, S.V., Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980.
79. Pollack, H.N., S.J. Hurter, and J.R. Johnson, Heat flow from the Earth's interior - Analysis of the global data set, Rev. Geophys., 31, 267-280, 1993.
80. Press, W.H., S.A. Teulolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes (2nd ed.), Cambridge Univ. Press, New York, 1992.
81. Rayleigh, Lord, On convective convective currents in a horizontal layer of fluid, when the higher temperature is on the under side, Philos. Mag., Ser. VI, 32, 529-546, 1916.
82. Ricard, Y., M. A. Richards, C. Lithgow-Bertelloni, and Y. LeStunff, A geodynamic model of mantle density heterogeneity, J. Geophys. Res., 98, 21,895-21,909, 1993.
83. Richter, F.M., Experiments on the stability of convection rolls in fluids whose viscosity depends on temperature, J. Fluid Mech., 89, 553-560, 1978.
84. Richter, F.M., H.C. Nataf, and S.F. Daly, Heat transfer and horizontally-averaged temperature of convection with large viscosity variations, J. Fluid Mech., 129, 173-192, 1983.
85. Schmeling, H., Compressible convection with constant and variable viscosity: The effect on slab formation, geoid, and topography, J Geophys. Res., 94, 12,463-12,481, 1989.
86. Schubert, G., Subsolidus convection in the mantles of terrestrial planets, Annu. Rev. Earth Planet. Sci., 7, 289-342, 1979.
87. Schubert, G., Numerical models of mantle convection, Annu. Rev. Fluid. Mech., 24, 359-394, 1992.
88. Schubert, G., and C.A. Anderson, Finite element calculations of very high Rayleigh number thermal convection, Geophys. J. R. Astron. Soc., 80, 575-601, 1985.
89. Schubert, G., D.J. Stevenson, and P. Cassen, Whole mantle cooling and the radiogenic heat source contents of the Earth and Moon, J. Geophys. Res., 85, 2531-2538, 1980.
90. Schubert, G., G.A. Glatzmaier, and B. Travis, Steady, three-dimensional, internally heated convection, Phys. Fluids A, 5, 1928-1932, 1993.
91. Sclater, J.G., C. Jaupart, and D. Galson, The heat flow through oceanic and continental crust and the heat loss of the Earth, Rev. Geophys., 18, 269-311, 1980.
92. Sharpe, H.N., and W.R. Peltier, Parameterized mantle convection and the Earth's thermal history, Geophys. Res. Lett., 5, 737-740, 1978.
93. Sleep, N.H., An analytic model for a mantle plume fed by a thermal boundary layer. Geophys. J. R. Astron. Soc., 90, 119-128, 1987.
94. Sleep, N.H., Hotspots and mantle plumes: Some phenomenology, J Geophys. Res., 95, 6715-6736, 1990.
95. Smolarkiewicz, P.K., A fully multidimensional positive definite advection transport algorithm with small implicit diffusion, J Comput. Phys., 54, 325-362, 1984.
96. Solomatov, V.S., Scaling of temperature dependent and stress-dependent viscosity convection, Phys. Fluids, 7, 266-274, 1995.
97. Solomon, S.C., S.E. Smrekar, D.L. Bindschadler, R.E. Grimm, W.M. Kaula, G.E. McGill, R.J. Phillips, R.S. Saunders, G. Schubert, S.W. Squyres, E.R. Stofan, Venus Tectonics - an overview of Magellan observations, J. Geophys. Res., 97, 13199-13255, 1992.
98. Stacey, F.D., Physics of the Earth, 3rd ed. , 513 pp., Brookfield, Kenmore, Queensland, Australia, 1992.
99. Stocker, R.L., and M.F. Ashby. On the rheology of the upper mantle, Rev. Geophys., 11, 391-426, 1973.
100. Su, W.-J., R.L. Woodward, and A.M. Dziewonski, Degree-12 model of shear velocity heterogeneity in the mantle, J. Geophys. Res., 99, 6945-6980, 1994.
101. Tackley, P.J., Effects of strongly temperature dependent viscosity on time-dependent, three-dimensional models of mantle convection, Geophys. Res. Lett., 20, 2187-2190, 1993.
102. Tackley, P.J., Three-dimensional models of mantle convection: influence of phase transitions and temperature dependent viscosity, Ph.D. thesis, Calif. Inst. of Technol., Pasadena, 1994.
103. Tackley, P.J., D.J. Stevenson, G.A. Glatzmaier, and G. Schubert, Effects of an endothermic phase transition at 670 km depth in a spherical model of convection in the Earth's mantle, Nature. 361, 699-704, 1993.
104. Tackley, P.J., D.J. Stevenson, G.A. Glatzmaier, and G. Schubert, Effects of multiple phase transitions in a 3-D spherical model of convection in the Earth's mantle, J. Geophys. Res., 99, 15877-15901, 1994.
105. Torrance, K.E., and D.L. Turcotte, Thermal convection with large viscosity variations, J. Fluid Mech., 47, 113-125, 1971.
106. Tozer, D.C., The present thermal state of the terrestrial planets, Phys. Earth Planet. Inter., 6, 182-197, 1972.
107. Travis, B.J., P. Olson, and G. Schubert, The transition from two-dimensional to three-dimensional planforms in infinite-Prandtl-number thermal convection, J. Fluid Mech., 216, 71-91, 1990a.
108. Travis, B., S. Weinstein, and P. Olson, Three-dimensional convection planforms with internal heat generation, Geophys. Res. Lett., 17, 243-246, 1990b.
109. Turcotte, D.L., and G. Schubert, Geodynamics: Applications of Continuum Physics to Geological Problems, John Wiley, New York, 1982.
110. van Keken, P.E., D.A. Yuen, and A.P. van den Berg, Implications for mantle dynamics from the high melting point of perovskite, Science, 264, 1437-1439, 1994.
111. Weertman, J., The creep strength of the Earth's mantle, Rev. Geophys. Space Phys., 8, 146-168, 1970.
112. Weertman, J., and J.R. Weertman, High temperature creep of rock and mantle viscosity, Annu. Rev. Earth Planet. Sci., 3, 293-315, 1975.
113. Weinstein, S.A., and U. Christensen, Convection planforms in a fluid with a temperature dependent viscosity beneath a stress-free upper boundary, Geophys. Res. Lett., 18, 2035-2038, 1991.
114. Weinstein, S.A., and P. Olson, Planforms in thermal convection with internal heat sources at large Rayeigh and Prandtl numbers, Geophys. Res. Lett., 17, 239-242, 1990.
115. Weinstein, S.A., and P.L. Olson, Thermal convection with non-Newtonian plates, Geophys. J. Int., 111, 515-530, 1992.
116. White, D.B., The planforms and onset of convection with a temperature dependent viscosity, J. Fluid Mech., 191, 247-286, 1988.
117. Whitehead, J.A., and B. Parsons, Observations of convection at Rayleigh numbers up to 760,000 in a fluid with large Prandtl number, Geophys. Astrophys. Fluid Dyn., 9, 201-217, 1978.
118. Young, R.E., Finite-amplitude thermal convection in a spherical shell, J. Fluid Mech, 63, 695-721, 1974.
119. Yuen, D.A., and S. Zhang, Equation of state and rheology in deep mantle convection, in Perovskite: A Structure of Great Interest to Geophysics and Materials Science, Geophys. Monogr., vol. 45, edited by A. Navrotsky and D.J. Weidner, pp. 131-137, AGU, Washington, D.C., 1989.
120. Yuen, D.A., D.M. Reuteler, S. Balachandar, V. Steinbach, A.V. Malevsky, and J.J. Smedsmo, Various influences on 3-dimensional mantle convection with multiple phase transitions, Phys. Earth Planet. Inter., 86, 185-203, 1994.